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The judges will look at whether the Lisbon Treaty - designed to improve decision-making in the EU - is not democratic, and therefore anti-constitutional, because it takes away power from Germany's parliament.

The case was brought conservative MP Peter Gauweiler as well as left-wing deputies from Die Linke political party.

An example given by Mr Gauweiler in written evidence takes the hypothetical case of a German environment minister wanting to get a ban on a particular light bulb.

If the initiative fails at national level in Bundestag, then the minister could present the idea in European Council, at EU leader level.

Support by other member states at this level could mean that the European Commission is asked to present a lightbulb proposal which eventually could get turned into EU law, despite Germany's parliament having rejected the proposal.

The hearing is being keenly followed by Chancellor Angela Merkel's government which has sent Foreign Minister Frank-Walter Steinmeier and Interior Minister Wolfgang Schaeuble to defend the government's case.

The challenge is politically important for Ms Merkel who has been a strong supporter of the treaty.

If Mr Gauweiler's case is upheld by the court, it would be a big blow to both the chancellor and the treaty's ratification process.

So far, the treaty has been through most of the process - it has been approved by both houses of parliament and signed by Germany's president. But the final step of ratification, handing the papers over in Rome, has been postponed pending the court decision.

The judgement is expected to be made in two to three months. But even if the court comes out in favour of the Lisbon Treaty, the process may not be over. Last month, a separate group handed in another complaint on the treaty, listing political and economic faults.

The court has yet to decide whether to take on the case.

Elsewhere, the fate of the treaty remains uncertain too. The Czech Republic has yet to begin ratification of the treaty, while Ireland is facing a second referendum on the document after its citizens rejected it last June.

Poland's President, meanwhile, has said he will not sign the treaty until it has been accepted in Ireland.

A number of centre-right MEPs are pushing for a secret ballot on a plenary vote that would make EU lawmakers more transparent and accountable to the public - in a move described as "absurd" by Transparency International.